The former Dunfermline player and manager is heading a working party who have taken control of the day-to-day running of the financially-stricken club.
Majority shareholder Gavin Masterton announced last night he will step down from the board, while chairman John Yorkston is to stand down as chairman and assume the role of honorary president on completion of a share offer, which has so far been delayed.
A sum of £134,000 is owed to Her Majesty's Revenue and Customs, although it is believed the amount is not due to be paid in one instalment.
On the task ahead, Leishman said: "It's the hardest thing I've ever done at this football club, it's the hardest thing I've got to try to achieve.
"Will I do it? I don't know. But I can't do it by myself, that's for sure.
"I've got a short period of time - maybe two weeks, maybe three, maybe four. I've got to remain positive.
"It's about the short-term survival of Dunfermline and the long-term future of the football club."
Some fans staged a protest outside East End Park on Saturday and supporters who had congregated outside the stadium today were invited inside to attend a press conference called to explain the new structure.
Leishman - who is set to meet with fans groups tonight - added: "The community of Dunfermline, the supporters of Dunfermline, have been divided.
"We are not a big enough club to have factions that are going everywhere. We can't be divided, we've got to be together.
"I want the club to be here for my grandchildren.
"We need money. There are pledges coming in. If we can get past the next two weeks, then the evolution starts again and we start to build for the future."
The Pars were hit with more financial problems yesterday when the Scottish Football Association issued them with a notice of complaint over failure to pay a debt to Hamilton, while Cowdenbeath are also owed money.
They also face the prospect of action from the Scottish Football League after PFA Scotland last week submitted a formal complaint after players were paid just 20% of their monthly wages in the latest in a series of delays.
Players have now received 60% of the payments due, with employees still owed £35,000 in total.
Leishman said: "We've got to prioritise now for the survival of the football club.
"The staff can't shut you down but HMRC can shut you down. We've got to get a solution to that and a solution for all the staff.
"The staff and players deserve so much credit for sticking by the club."
On the issue of HMRC, he added: "We are asking business people to put money in and support us to get that initial problem solved.
"We've got people who pledged money and it's about turning pledges into donations."
A share issue, which it is hoped will raise up to £500,000, is set to be launched within days.
Accountant Steven Taylor, who is part of the steering group, said: "At Hearts a few months back, the cry went out that their next home game could be their last game.
"I'm not suggesting we are quite at that point but we're rapidly heading in that direction.
"We desperately need cash in. The share issue, which is hopefully going to be launched in the next couple of days, is only part of the exercise.
"There is going to have to be cost-cutting and we will have to operate with a much smaller squad next year.
"There are other elements, getting a bit smarter on the commercial side and looking at other overheads and costs as well.
"But we are rapidly running out of time."